Search results for "Finite dimensional approximation"

showing 3 items of 3 documents

Adaptive control of a seven mode truncation of the Kolmogorov flow with drag

2009

Abstract We study a seven dimensional nonlinear dynamical system obtained by a truncation of the Navier–Stokes equations for a two dimensional incompressible fluid with the addition of a linear term modelling the drag friction. We show the bifurcation sequence leading from laminar steady states to chaotic solutions with increasing Reynolds number. Finally, we design an adaptive control which drives the state of the system to the equilibrium point representing the stationary solution.

D'Alembert's paradoxEquilibrium pointTruncationGeneral MathematicsApplied MathematicsMathematical analysisGeneral Physics and AstronomyReynolds numberAdaptive controlStatistical and Nonlinear PhysicsLaminar flowDrag equationFinite dimensional approximationPhysics::Fluid Dynamicssymbols.namesakeClassical mechanicsDragsymbolsBifurcationReynolds-averaged Navier–Stokes equationsMathematics
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Analysis and control of a seven mode truncation of the Kolmogorov flow with drag.

2008

The transition from laminar to chaotic motion in a viscous fluid flow is investigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov flow with drag friction. Analytical expressions of the bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynoplds number is increased for fixed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is obtained through a model reference approach which makes the control global.

Finite dimensional approximation adaptive control
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A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control

2009

The transition from laminar to chaotic motions in a viscous °uid °ow is in- vestigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov °ow with drag friction. An- alytical expressions of the Hopf bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynolds num- ber is increased for ¯xed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is ob- tained through a model reference approach which makes the control global. Finally, the e®ectiveness of this control strategy is numerically illustra…

Period-doubling bifurcationEquilibrium pointHopf bifurcationTruncationMathematical analysisReynolds numberLaminar flowDynamical systemPhysics::Fluid Dynamicssymbols.namesakeClassical mechanicsDragsymbolsKolmogorov flow finite dimensional approximation adaptive controlMathematics
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